The values p and q in the quadratic expression 2x² - px + q are determined by throwing two standard fair cubical dice, one red and one blue.

p is given by the value shown by the red die and q is given by the value shown on the blue die.

What is the probability that the equation 2x² - px + q = 0 will have a solution that is a prime number?

hits=0;
for p=1:6
  for q=1:6
    disc=p^2-4*2*q;
    if disc>=0
      hit=false;
      s1=(p+sqrt(disc))/4;
      if s1>0 && s1==round(s1)
        if isprime(s1)
          hit=true;
        end
      end
      s2=(p-sqrt(disc))/4;
      if s2>0  && s2==round(s2)
        if isprime(s2)
          hit=true;
        end
      end
      if hit
        hits=hits+1;
        fprintf('%d %d %d %5f\n',p,q,s1,s2)
      end
    end
  end
end
hits/36

         solutions 

p q 1     2

5 2 2 0.500000

6 4 2 1.000000

only two have prime solutions

ans =

    0.0556

Posted by Charlie on 2024-02-21 23:06:05